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21 January, 07:15

Suppose that a random variable has a standard normal distribution. Use a standard normal table such as this one to determine the probability that is between - 1 and 0.67. Give your answer in decimal form, precise to at least three decimal places.

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  1. 21 January, 07:17
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    The probability That is between - 1 and 0.67 is 0.58991

    Step-by-step explanation:

    * Lets explain how to solve it

    - A random variable has a standard normal distribution

    - Z-scores are - 1 and 0.67

    - We need to find the probability that is between them by using the

    standard normal table

    - Search in the table of the standard normal distribution for the

    corresponding area of - 1 and corresponding area of 0.67

    - From the standard normal distribution table we find that

    ∵ The corresponding area which represents z = - 1 is 0.15866

    ∵ The corresponding area which represents z = 0.67 is 0.74857

    - To find the probability between - 1 and 0.67 find the difference

    between the corresponding areas of - 1 and 0.67

    ∵ z = - 1 represented by 0.15866

    ∵ z = 0.67 represented by 0.74857

    ∴ The difference of the corresponding areas is:

    0.74857 - 0.15866 = 0.58991

    ∴ The probability that is between - 1 and 0.67 is 0.58991
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